Mixed hyper-digital logic

online since July 2007

Abstract

In previous texts
(e.g. [1]),
we defined
bit table sets
and their
bit table algebras.
Each one was fixed in the sense that carrier A and degree k were constants in the given context. We now ask for possibilities to define mixed algebras, in particular on

the mixed carrier set Bk(A), which is the union of the
for all subsets S of A

the mixed degree set B*(A), which is the union of the
,
for all degrees k

the (general or mixed) bit table set B(A), which is the union of the
,
for all subsets S of A and all degrees k

The minimal condition we put on all these potential generalization will be, that they are proper expansions of all the fixed algebras they cover.

Similar to these versions of bit table algebras, we try to generalize the different "fixed" hyper-propositional formula algebras
by defining a mixed hyper-propositional formula algebraF(A).